Question: Simplify. Rewrite the expression in the form $7^n$. $7^2\cdot 7^6=$
Explanation: $\begin{aligned} 7^2\cdot 7^6&=7^{2+6} \\\\ &=7^{8} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 7^2\cdot 7^6&=\underbrace{7\cdot 7}_\text{2 times}\cdot\underbrace{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7}_\text{6 times} \\\\\\ &=\underbrace{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7}_\text{8 times} \\\\ &=7^{8} \end{aligned}$ In conclusion, $7^2\cdot 7^6=7^{8}$.